Seminar Abstracts (Fall 2008)

Francois-Xavier Vialard, ENS Cachan
From the Hamiltonian formulation of image matching to a general shape diffusion model
Abstract We will discuss the Hamiltonian point of view for shape matching and image matching through diffeomorphisms. After a short introduction to Hamiltonian systems, we will discuss some deterministic issues with image matching within this framework. Especially, we will deal with discontinuous images (BV functions) in the LDDMM framework. The second part of the talk will present a stochastic perturbation of the Hamiltonian equations for the Landmark case. Our result is to extend this stochastic model in a consistent way to the case of shapes.

Marc Yor, University Pierre et Marie Curie, Paris
An interpretation and some extensions of Black-Scholes formula via last passage times of martingales
Abstract: The put quantity associated to a continuous positive local martingale is closely related with the distribution function of a last passage time of this martingale.

Tim Leung, Johns Hopkins University
Exponential Utility Hedging with Optimal Stopping and Application to ESO Valuation
Absract: We study the problem of hedging early exercisable (American) options with respect to exponential utility within a general incomplete market model. This leads to the study of a joint stochastic control and optimal stopping problem. We construct a duality formula involving relative entropy minimization and optimal stopping, and characterize the optimal exercising strategy. Furthermore, we consider claims with multiple exercises, and static-dynamic hedges of American claims with other European and American options. The problem is important for accurate valuation of employee stock options (ESOs), and we demonstrate this in a standard diffusion model. We find that incorporating static hedges with market-traded options induces the holder to delay exercises, and increases the ESO cost to the firm. The related paper can be found here.

Edward Scheinerman, Johns Hopkins University
Random Threshold Graphs
Abstract: A \emph{random threshold graph} is a simple graph with vertex set $\{1,2,\ldots,n\}$ that is generated as follows: Let $x_1,x_2,\ldots,x_n$ be $n$ values chosen uniformly and independently from $[0,1]$. Join distinct vertices $u$ and $v$ by an edge if and only if $x_u + x_v > 1$. We discuss various properties of random threshold graphs. For example, the probability that a random threshold graph on $n$ vertices has a Hamiltonian cycle is asymptotically $1/\sqrt{2\pi n}$. This is joint work with Elizabeth Reilly.
(Click here if you see dollar signs).

Mark Huber, Duke University
Perfect simulation of Matérn Type III point processes
Absract: Spatial data are often more dispersed than would be expected if the points were independently placed. Such data can be modeled with repulsive point processes, where the points appear as if they are repelling one another. Various models have been created to deal with this phenomenon. Matérn created three algorithms that generate repulsive processes. Here, Matérn Type III processes are used to approximate the likelihood and posterior values for data. Perfect simulation methods are used to draw auxilliary variables for each spatial point that are part of the type III process.

William Christensen, Brigham Young University
Identifying pollution source locations for air quality monitoring
Abstract The pollution source apportionment (PSA) problem involves quantifying the impact of major sources of pollution on air quality. The identification of pollution source directions is an important part of PSA. Estimated source directions are used both as inputs to a Bayesian source apportionment analysis, and as part of a post-analysis check to associate identified pollution factors with potential pollution sources. We consider two approaches for source location identification which can be used in different settings. The first requires wind direction data measured at the air quality receptor and makes use of statistical and/or deterministic (AERMOD) models for chemical transport of particulate matter from source to receptor. The second makes use of HYSPLIT back-trajectory estimates and a kriging estimator which filters heterogeneous measurement errors.

Stephen Fienberg, Carnegie Mellon University
Forensic Science More Scientific: Statistics and the Evaluation Forensic Evidence
Abstract Forensic science is under increasing attack, especially in the U.S.This is the consequence of the confluence of a number of elements including (a) continued revelations of wrongful convictions linked to faulty forensic evidence, (b) the resounding success of DNA and other genetic evidence in a forensic context, and (c) the “CSI Effect”—the expectation of infallible high tech forensic tools that are part of the popular weekly crime show, Crime Scene Investigation. In this talk I will describe a potpourri of forensic tools (e.g., the polygraph, eyewitness testimony, traditional fingerprinting, and new computer forensic tools), legal cases in which they arise, some assessments of their accuracy especially in reports from the National Research Council. In particular, I focus on the role statistics plays in their evaluation and legal credibility.

Seth Guikema, Johns Hopkins University
Statistical Assessment of the Influence of Climate Change and Climate Variability on Hurricane Hazards
Abstract There is significant concern about the possibility of global climate change increasing hurricane hazards in the U.S. However, there is also considerable disagreement about the relationship between climate change and changes in hurricane hazards. For example, recent literature has suggested that climate change may (1) increase the number of hurricanes making landfall, (2) decrease the total number of hurricanes making landfall but increase the intensity of the strongest storms, or (3) have little influence on hurricane hazards in the U.S. Past statistical analyses have focused on a relatively small number of parameters for describing the climate and climate change. They have not fully accounted for the confounding effects of climate cycles occurring on multiple time scales that are thought to substantially influence hurricane hazards. This talk will summarize past statistical research focused on the climate change - hurricane relationship. It will then summarize ongoing work using tree-based data mining methods to more fully explore and understand the complex relationship between climate variability, climate change, and hurricane hazards in the U.S. This work is the first step in a multi-year project focusing on modeling the influence of climate change on hurricane hazards and the impacts that this may have on changes in risk to critical infrastructure systems in the coastal U.S. Ample time will be planned for feedback and audience interaction.

Natalia Trayanova, Johns Hopkins University
Predictive Models of the Heart in Health and Disease
Abstract: Simulating cardiac electromechanical function is one of the most striking examples of a successful integrative multi-scale modeling approach applied to a living system directly relevant to human disease. Today, thanks to nearly fifty years of research in the field and the rapid progress of high-performance computing, we stand at the threshold of a new era: anatomically-detailed tomographically- reconstructed models that integrate from the ion channel or sarcomere to the electromechanical interactions in the intact heart are being developed. Such models, while still in its infancy, hold high promise for interpretation of clinical and physiological measurements in terms of cellular mechanisms; for improving the basic understanding of the mechanisms of dysfunction in disease conditions, such as reentrant arrhythmias, myocardial ischemia, and heart failure; and for the development and performance optimization of medical devices, ultimately enabling manufacturers to predict device and procedure performance and outcome prior to clinical trials. Attempt is made to extend these models beyond electromechanics and include regulatory processes such as energy metabolism and signal transduction. Here we provides specific examples of the state-of-the-art in cardiac integrative modeling, including 1) uncovering the role of ventricular structure in defibrillation; 2) improving ventricular ablation procedure by using MRI reconstructed heart geometry and structure to investigate the reentrant circuits formed in the presence of an infarct scar; 3) understanding the origin of mechanically-induced ventricular premature beats in acute regional ischemia, and others.

Gregory Duffee, Johns Hopkins University
Information in (and not in) the term structure
Abstract: Casual intuition says that today’s term structure reflects all information investors have about expected future yields. However, this is not required by finance theory, nor is it consistent with observed Treasury yield behavior. Kalman filter estimation uncovers a factor that has an almost imperceptible effect on yields, but has clear forecast power for future short-term interest rates and substantial forecast power for future excess bond returns. The factor appears to be related to short-run fluctuations in economic activity.

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